Seasonal Adjustment

dateutils works with the package seasonal to seasonally adjust monthly and quarterly data in data.table format. For example, suppose we wanted to seasonally adjust gdp and advance retail sales in our quarterly dataset. We can do so as follows:

fred_sa <- seas_df_long(fred_quarterly, sa_names = c("gdp constant prices", "advance retail sales"),
                        transfunc = 'auto')

## Model used in SEATS is different: (1 2 3)(0 0 1)

gdp <- rbind(fred_quarterly[series_name == "gdp constant prices", .(ref_date, series_name, value)],
             fred_sa$values_sa[series_name == "gdp constant prices sa"])
gdp <- dcast(gdp, ref_date ~ series_name, value.var = "value")
matplot(gdp$ref_date, gdp[,-1,with=FALSE], type = 'l')

Of course, these data are already seasonally adjusted, so adjusting again makes little difference.

Mixed frequency data

dateutils is built around handling mixed frequency data. In particular, the package allows you to easily build mixed frequency models incorporating all available information to date without worrying about bridge equations. We accomplish this by identifying the pattern of missing observations in the tail of the data, and replicating that pattern in the historical data, to generate contemporaneous right hand side (RHS) variables, as well as the usual lagged RHS variables. The resulting data set is uniform frequency, allowing the use of any of the standard statistical models available in R. We can illustrate this process again using the built in data fred. We will construct a nowcast of GDP, the lowest frequency variable in the data, using the other the other three monthly, weekly, and daily series. To begin, we can look at the tail of each of the four series.

tail(fred[series_name == "gdp constant prices"], 2)

##            series_name   ref_date    value       country   pub_date pub_lag
## 1: gdp constant prices 2020-09-30 18596.52 united states 2020-10-30      30
## 2: gdp constant prices 2020-12-31 18794.43 united states 2021-01-29      29

The last observation we have for GDP is Q4 2020, thus our nowcast will be for Q1 2021 (the as_of date for this data is February 26 2021, which was a Friday). Looking next at the monthly data

tail(fred[series_name == "advance retail sales"], 4)

##             series_name   ref_date  value       country   pub_date pub_lag
## 1: advance retail sales 2020-10-31 493991 united states 2020-11-18      18
## 2: advance retail sales 2020-11-30 488652 united states 2020-12-17      17
## 3: advance retail sales 2020-12-31 484782 united states 2021-01-16      16
## 4: advance retail sales 2021-01-31 520162 united states 2021-02-18      18

In this case, our contemporaneous data will include the first month in the quarter. Lagged data (i.e. Q4 2020) is complete. Looking next at weekly data

tail(fred[series_name == "initial jobless claims"])

##               series_name   ref_date  value       country   pub_date pub_lag
## 1: initial jobless claims 2021-01-01 781000 united states 2021-01-21      20
## 2: initial jobless claims 2021-01-08 904000 united states 2021-01-28      20
## 3: initial jobless claims 2021-01-15 886000 united states 2021-02-04      20
## 4: initial jobless claims 2021-01-22 836000 united states 2021-02-11      20
## 5: initial jobless claims 2021-01-29 837000 united states 2021-02-18      20
## 6: initial jobless claims 2021-02-05 863000 united states 2021-02-25      20

Here we observe the first six weeks of the quarter for Q1 2021. And finally, for daily data

tail(fred[series_name == "t bill spread 10y 3m"], 3)

##             series_name   ref_date value       country   pub_date pub_lag
## 1: t bill spread 10y 3m 2021-02-23  1.33 united states 2021-02-24       1
## 2: t bill spread 10y 3m 2021-02-24  1.35 united states 2021-02-25       1
## 3: t bill spread 10y 3m 2021-02-25  1.50 united states 2021-02-26       1

We observe through February 25th, which in this case means 37 observations (values for weekends are not observed). The function process_MF() operates by calculating how many observations we have for the contemporaneous (nowcast, or one step ahead of the last observation of left hand side (LHS) data) period for each series in the data. In this case, since we observe the first 37 days for t bill spreads, the contemporaneous variable for t bill spreads will aggregate the first 37 observations in the historical data as well. If an early observation was missing, say the 22nd, than this observation would also be omitted when calculating historical aggregates. This contemporaneous variable will be appended with a 0 in the resulting data; the variable at one lag will be appended with a 1, and so on. If lagged periods are missing in the tail of the data the pattern of missing observations will be replicated in the same way.

We can verify this approach by running the function.

MF <- process_MF(fred[series_name == "gdp constant prices"], fred[series_name != "gdp constant prices"],
                 LHS_lags = 3, RHS_lags = 3) 

Here we are using three lags of LHS variables and three lags of RHS varialbes. Note that data must be entered in long format. Aside from being more efficient for mixed frequency data (i.e. avoiding a lot of NA entries for low frequency data), this allows for backtesting by censoring data using the as_of argument. Required columns are ref_date, series_name, and value. If your data has different column names, you will have to inform the function using the arguments date_name, id_name, and value_name. If you wish to backtest your data using as_of you must also include the column pub_date, or inform the function which column contains publication dates using pub_date_name.

By default process_MF() returns data in long format. If you wish to have the data in matrix format, you can set return_dt = FALSE. Since dateutils is built on data.table, we can also transform the output to wide format as follows

library(data.table)
dt_wide <- dcast(MF, ref_date ~ series_name, value.var = "value")
tail(dt_wide)

##      ref_date gdp constant prices 0 gdp constant prices 1 gdp constant prices 2
## 1: 2020-09-30              18596.52              17302.51              19010.85
## 2: 2020-12-31              18794.43              18596.52              17302.51
## 3: 2021-03-31                    NA              18794.43              18596.52
## 4: 2021-06-30                    NA                    NA              18794.43
## 5: 2021-09-30                    NA                    NA                    NA
## 6: 2021-12-31                    NA                    NA                    NA
##    gdp constant prices 3 advance retail sales 0 initial jobless claims 0
## 1:              19253.96                 481627                1243833.3
## 2:              19010.85                 493991                 779000.0
## 3:              17302.51                 520162                 851166.7
## 4:              18596.52                     NA                       NA
## 5:              18794.43                     NA                       NA
## 6:                    NA                     NA                       NA
##    t bill spread 10y 3m 0 advance retail sales 1 initial jobless claims 1
## 1:              0.5086486               433592.3                2716615.4
## 2:              0.7275676               486223.3                1041076.9
## 3:              1.0983784               489141.7                 783000.0
## 4:                     NA               520162.0                 851166.7
## 5:                     NA                     NA                       NA
## 6:                     NA                     NA                       NA
##    t bill spread 10y 3m 1 advance retail sales 2 initial jobless claims 2
## 1:              0.5453968               451492.3                 867846.2
## 2:              0.5371875               433592.3                2716615.4
## 3:              0.7716129               486223.3                1041076.9
## 4:              1.0983784               489141.7                 783000.0
## 5:                     NA               520162.0                 851166.7
## 6:                     NA                     NA                       NA
##    t bill spread 10y 3m 2 advance retail sales 3 initial jobless claims 3
## 1:              0.2609677               457066.3                 218923.1
## 2:              0.5453968               451492.3                 867846.2
## 3:              0.5371875               433592.3                2716615.4
## 4:              0.7716129               486223.3                1041076.9
## 5:              1.0983784               489141.7                 783000.0
## 6:                     NA               520162.0                 851166.7
##    t bill spread 10y 3m 3
## 1:              0.1843548
## 2:              0.2609677
## 3:              0.5453968
## 4:              0.5371875
## 5:              0.7716129
## 6:              1.0983784

Checking the result for advance retail sales is simple as we are only using the first observation in the quarter. Thus for Q1 2021 it is 520162; for the first month in Q4 2020 it is 493991. process_MF() allows for multiple LHS variables, but all LHS variables must be the same frequency (i.e. quarterly, monthly, etc.).

So far we have transformed our mixed frequency data into meaningful, up-to-date uniform frequency data. However, several series are still non-stationary. Before modeling, will will have to process these data to ensure stationarity and thereby consistent results. We can do this using the function process(). Instructions on how to process the data are in a library file, in this case called fredlib.

print(fredlib)

##          country            series_name needs_SA frequency     type        unit
## 1: united states   advance retail sales        0   monthly business USD Million
## 2: united states    gdp constant prices        0 quarterly      gdp USD Billion
## 3: united states initial jobless claims        0    weekly   labour    Thousand
## 4: united states   t bill spread 10y 3m        0     daily  markets     percent
##    source take_logs take_diffs
## 1:   FRED         1          1
## 2:   FRED         1          1
## 3:   FRED         1          0
## 4:   FRED         0          0

Required columns are series_name, take_logs, and take_diffs. Optional columns are country, needs_SA, detrend, center, and scale. Other columns, such as type above, are ignored. Unique identification of each series can come from series_name alone or series_name and country pairs. Note that when we transformed the mixed frequency data using process_MF() we appended series names with 0 for contemporaneous data, 1, for one lag, and so on. By default, the argument ignore_numeric_names = TRUE so that process() correctly identifies each series from the library fredlib.

dt_processed <- process(MF, fredlib)
print(dt_processed[1:4])

##      ref_date           series_name      value level_value low_frequency_trend
## 1: 2000-03-31 gdp constant prices 0         NA    9.466855         0.003471811
## 2: 2000-06-30 gdp constant prices 0  1.0596728    9.485001         0.003844023
## 3: 2000-09-30 gdp constant prices 0 -0.1389716    9.486336         0.004295838
## 4: 2000-12-31 gdp constant prices 0  0.1701025    9.492545         0.004719393
##    standardize_center standardize_scale
## 1:      -0.0009596734        0.01440224
## 2:      -0.0009596734        0.01440224
## 3:      -0.0009596734        0.01440224
## 4:      -0.0009596734        0.01440224

Output from dt_processed includes all of the information one would need to convert data back to levels. If we had seasonally adjusted any of the series, output would also include the column seasonal_factor.

Now that we have stationary, uniform frequency data, we can use any of the standard econometric models. For example,

X <- dcast(dt_processed, ref_date ~ series_name, value.var = "value")
out <- lm(`gdp constant prices 0` ~ `advance retail sales 0` + 
          `initial jobless claims 0` + `t bill spread 10y 3m 0`, data = X)
summary(out)

## 
## Call:
## lm(formula = `gdp constant prices 0` ~ `advance retail sales 0` + 
##     `initial jobless claims 0` + `t bill spread 10y 3m 0`, data = X)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.25144 -0.21286 -0.05089  0.26860  1.30541 
## 
## Coefficients:
##                             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                 0.001103   0.047947   0.023    0.982    
## `advance retail sales 0`    0.836399   0.049131  17.024   <2e-16 ***
## `initial jobless claims 0` -0.221607   0.052786  -4.198    7e-05 ***
## `t bill spread 10y 3m 0`    0.064252   0.048809   1.316    0.192    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4365 on 79 degrees of freedom
##   (5 observations deleted due to missingness)
## Multiple R-squared:  0.8164, Adjusted R-squared:  0.8094 
## F-statistic: 117.1 on 3 and 79 DF,  p-value: < 2.2e-16

Other Functions

dateutils additionally exports a large number of small functions which names that are hopefully self explanatory. We can see the complete list as follows:

ls("package:dateutils")

##  [1] "Diff"                    "add_forecast_dates"     
##  [3] "agg_to_freq"             "agg_to_freq_wide"       
##  [5] "allNA"                   "all_finite"             
##  [7] "any_finite"              "can_seasonal"           
##  [9] "col_to_list"             "comp_form"              
## [11] "count_obs"               "day"                    
## [13] "end_of_period"           "end_of_year"            
## [15] "extract_basic_character" "extract_character"      
## [17] "extract_numeric"         "fill_forward"           
## [19] "first_of_month"          "first_of_quarter"       
## [21] "first_previous_quarter"  "fred"                   
## [23] "fredlib"                 "get_data_frq"           
## [25] "get_from_list"           "index_by_friday"        
## [27] "is_in"                   "last_in_month"          
## [29] "last_in_quarter"         "last_in_week"           
## [31] "last_in_year"            "last_obs"               
## [33] "limit_character"         "long_run_var"           
## [35] "match_index"             "match_ts_dates"         
## [37] "mean_na"                 "month_days"             
## [39] "number_finite"           "numdum"                 
## [41] "pct_chng"                "pct_response"           
## [43] "process"                 "process_MF"             
## [45] "process_wide"            "rollmax"                
## [47] "rollmean"                "rollmin"                
## [49] "row_to_list"             "run_sa"                 
## [51] "sd_na"                   "seas_df_long"           
## [53] "seas_df_wide"            "spline_fill"            
## [55] "spline_fill_trend"       "stack_obs"              
## [57] "sum_na"                  "to_ts"                  
## [59] "total_response"          "try_detrend"            
## [61] "try_sa"                  "try_trend"              
## [63] "ts_to_df"

As a few more examples, we can find the last date of a time period using one of the following functions:

dates <- seq.Date(from = as.Date("2021-01-01"), to = as.Date("2021-06-30"), by = "day")
weekvals <- end_of_period(dates, period = "week")
unique(weekdays(weekvals))

## [1] "Friday"

or, to shift dates forward one month,

monthvals <- end_of_period(dates, period = "month", shift = 1)
unique(monthvals)

## [1] "2021-02-28" "2021-03-31" "2021-04-30" "2021-05-31" "2021-06-30"
## [6] "2021-07-31"